OVERVIEW
[0001] Aspects of various embodiments are directed to radar apparatuses/systems and related
methods.
[0002] In certain radar signaling applications including but not limited to automotive and
autonomous vehicle applications, high spatial resolution may be desirable for detecting
and distinguishing objects which are perceived as being located at the similar distances
and/or moving at similar velocities. For instance, it may be useful to discern directional
characteristics of radar reflections from two or more objects that are closely spaced,
to accurately identify information such as location and velocity of the objects.
[0003] Virtual antenna arrays have been used to mitigate ambiguity issues with regards to
apparent replicas in discerned reflections as indicated, for example, by the amplitudes
of corresponding signals as perceived in the spatial resolution spectrum (e.g., amplitudes
of main lobes or "grating lobes"). But even with many advancements in configurations
and algorithms involving virtual antenna array, radar-based detection systems continue
to be susceptible to ambiguities and in many instances yield less-than optimal or
desirable spatial resolution. Among these advancements, virtual antenna arrays have
been used with multiple-input multiple-output (MIMO) antennas among other type of
known arrays to achieve a higher spatial resolution, but such approaches can be challenging
to implement successfully, particularly in rapidly-changing environments such as those
involving automobiles travelling at relatively high speeds.
[0004] These and other matters have presented challenges to efficiencies of radar implementations,
for a variety of applications.
SUMMARY
[0005] Various example embodiments are directed to issues such as those addressed above
and/or others which may become apparent from the following disclosure concerning radar
devices and systems in which objects are detected by sensing and processing reflections
or radar signals for discerning location information and related information including
as examples, distance, angle-of-arrival and/or speed information.
[0006] In certain example embodiments, aspects of the present disclosure are directed to
radar-based processing circuitry configured to solve for a sparse array AoA (angle
of arrival) estimation problem in which ambiguities may be recognized and overcome
for an accurate AoA estimation while also accounting for data processing throughput
and computation resources. More specific aspects of the present disclosure are directed
to overcoming the estimation problem by carrying out a set of steps which help to
account for measurement errors and noise by iteratively updating measurement-error
and noise parameters, and with the set up steps using a matrix-based model in which
each of the possible spectrum support vectors is drawn from a distinct distribution,
for example, as may be used in known Sparse Bayesian Models in automatic relevance
determination methodologies.
[0007] In more specific example embodiments, the present disclosure is directed to a method
and/or an apparatus involving a radar system having a logic circuit and a memory array
(e.g., MIMO array in which at least one uniform sparse linear array may be embedded)
for processing radar reflection signals. Various steps or actions carried out by the
radar logic circuitry include generating output data indicative of the reflection
signals' amplitudes, and discerning angle-of-arrival information for the output data
for the output data by correlating the output data with an iteratively-refined estimate
of a sparse spectrum support vector ("support vector"). The estimate includes: iteratively
updating of a set of parameters associated with previous values of the support vector
including a covariance estimate, and a statistical expectation among a plurality of
support vectors; and pruning, for each iterative update, certain of the plurality
of support vectors having amplitudes which are insignificant relative to the statistical
expectation of the support vector of in a preceding iteration.
[0008] In other more specific examples, the above examples may involve one or more of the
following aspects (e.g., such additional aspects being used alone and/or in any of
a variety of combinations). The sparse spatial frequency support vector may be processed
as a random variable using a matrix-based model, and with the matrix-based model processed
by Cholesky decomposition with each iterative update, so as to reduce computational
burdens. The steps may be carried out sequentially, without inversion of a matrix
in the matrix-based model, with the update of the statistical expectation of the support
vector following the update of the covariance estimate of the support vector, and
the update of the noise variance parameter following the update of the statistical
expectation of the support vector. Further, the set of parameters may include a noise
variance parameter, and a precision vector associated with a random variable τ such
that the conditional probability of the support vector in a current iterative update,
given τ, is a joint Gaussian distribution, and the conditional probability of τ itself
is a Gamma distribution with multiple parameters chosen to promote sparse outcomes
for the iteratively-refined estimate.
[0009] In the above examples and/or other specific example embodiments, further aspects
are as follows. The iterative updating of the parameters may be carried out over an
increasing iteration count which stops upon reaching or satisfying a threshold criteria
which may be a function of the multiple parameters and/or a function of a measurement
error having a Gaussian distribution. In response to the threshold criteria, resultant
data may be generated to provide the discerned angle-of-arrival information as an
output. Also, the measurement error may correspond to an error probability given the
constraint of the support vector after its most recent iterative update. Further,
to increase the accuracy, the array may have at least two embedded arrays, each of
which is being associated with a unique antenna-element spacing from among a set of
unique co-prime antenna-element spacings.
[0010] In an example embodiment of the present disclosure, an apparatus is provided, the
apparatus comprising: a radar circuit to receive reflection signals, in response to
transmitted radar signals, as reflections from objects; and computer processing circuitry
to process data corresponding to the reflection signals via a memory array and, in
response, to generate output data indicative of signal magnitude associated with the
reflection signals, and to discern angle-of-arrival information for the output data
by correlating the output data with an iteratively-refined estimate of a sparse spatial
frequency support vector ("support vector") indicative of a correlation peak for the
output data, the iteratively-refined estimate generated by: iteratively updating of
a set of parameters associated with previous values of the support vector including
a covariance estimate of the support vector, and a statistical expectation of the
support vector over a plurality of spectrum-related support vectors; and pruning,
for each iterative update, certain of the plurality of spectrum-related support vectors
having respective amplitudes which are insignificant relative to the statistical expectation
of the support vector derived in a preceding iteration.
[0011] In one or more embodiments, the sparse spatial frequency support vector is processed
as a random variable using a matrix-based model, and wherein the matrix-based model
is processed by Cholesky decomposition with each iterative update.
[0012] In one or more embodiments, the set of parameters includes a noise variance parameter,
wherein the sparse spatial frequency support vector is processed as a random variable
using a matrix-based model, and wherein the steps are carried out sequentially, without
inversion of a matrix in the matrix-based model, with the update of the statistical
expectation of the support vector following the update of the covariance estimate
of the support vector, and an update of the noise variance parameter following the
update of the statistical expectation of the support vector.
[0013] In one or more embodiments, the set of parameters includes a noise variance parameter
and further includes a precision vector associated with a random variable τ such that
a conditional probability of the support vector in a current iterative update, given
τ, is a joint Gaussian distribution, and a conditional probability of τ itself is
a Gamma distribution with multiple parameters chosen to promote sparse outcomes for
the iteratively-refined estimate.
[0014] In one or more embodiments, the iterative updating of the set of parameters is carried
out over an increasing iteration count which stops as a function of the multiple parameters.
[0015] In one or more embodiments, the iterative updating of the set of parameters is carried
out over an increasing iteration count which stops as a function of a measurement
error having a Gaussian distribution.
[0016] In one or more embodiments, the measurement error corresponds to a probability of
error given the support vector after its most recent iterative update.
[0017] In one or more embodiments, the computer processing circuitry is to iteratively update
the set of parameters over an increasing iteration count which ceases upon reaching
or satisfying a threshold criteria and, in response, to the threshold criteria, generate
resultant data corresponding to the discerned angle-of-arrival information for the
output data.
[0018] In one or more embodiments, the statistical expectation corresponds to a mean, or
average of the plurality of spectrum-related support vectors associated with a current
iteration.
[0019] In one or more embodiments, the statistical expectation corresponds to a range corresponding
to a subset of the plurality of spectrum-related support vectors associated with a
current iteration, wherein the subset accounts for or includes a mean.
[0020] In one or more embodiments, the memory array is or includes a multi-input multi-output
virtual array has at least one embedded uniform sparse linear arrays being associated
with a unique antenna-element spacing.
[0021] In one or more embodiments, the memory array is or includes a multi-input multi-output
virtual array having at least two embedded uniform sparse linear arrays, each of which
is being associated with a unique antenna-element spacing from among a set of unique
co-prime antenna-element spacings.
[0022] In one or more embodiments, the radar circuit includes sets antenna elements spaced
for radar signal transmissions and in response, reception of reflections from the
radar signal transmissions.
[0023] In one or more embodiments, the radar circuit includes front-end analog circuitry
for radar signal transmissions and in response, reception of reflections from the
radar signal transmissions, and further includes analog-to-digital and/or digital-to-analog
conversion circuitry to communicatively couple the front-end analog circuitry with
the computer processing circuitry.
[0024] In another embodiment of the present disclosure, a computer-implemented method is
provided. The method is in a radar system circuit. Thus, the method may be configured
for the radar system and/or may be carried out by the radar system. The method comprising:
generating, via the logic circuit, output data indicative of signal magnitude associated
with the reflection signals, and discerning angle-of-arrival information for the output
data for the output data by correlating the output data with an iteratively-refined
estimate of a sparse spatial frequency support vector ("support vector") indicative
of a correlation peak for the output data, the iteratively-refined estimate generated
by: iteratively updating of a set of parameters associated with previous values of
the support vector including a covariance estimate of the support vector, and a statistical
expectation of the support vector over a plurality of spectrum-related support vectors;
and pruning, for each iterative update, certain of the plurality of spectrum-related
support vectors having respective amplitudes which are insignificant relative to the
statistical expectation of the support vector of in a preceding iteration.
[0025] In another embodiment of the present disclosure, a method for use in an apparatus
which includes a radar circuit and computer processing circuitry is provided. The
method comprising: receiving, in response to transmitted radar signals, reflection
signals as reflections from objects; and in the computer processing circuitry, processing
data corresponding to the reflection signals via a memory array, generating, in response,
output data indicative of signal magnitude associated with the reflection signals,
and discerning angle-of-arrival information for the output data for the output data
by correlating the output data with an iteratively-refined estimate of a sparse spatial
frequency support vector ("support vector") indicative of a correlation peak for the
output data, the iteratively-refined estimate generated by: iteratively updating of
a set of parameters associated with previous values of the support vector including
a covariance estimate of the support vector, and a statistical expectation of the
support vector over a plurality of spectrum-related support vectors; and pruning,
for each iterative update, certain of the plurality of spectrum-related support vectors
having respective amplitudes which are insignificant relative to the statistical expectation
of the support vector of in a preceding iteration.
[0026] In one or more embodiments, the sparse spatial frequency support vector is processed
as a random variable using a matrix-based model or mathematical relationship, and
wherein the matrix-based model is processed by Cholesky decomposition with each iterative
update.
[0027] In one or more embodiments, the steps of processing, generating, discerning, iteratively
updating and pruning are carried out sequentially with the update of the statistical
expectation of the support vector following the update of the covariance estimate
of the support vector, and an update of a noise variance parameter following the update
of the statistical expectation of the support vector.
[0028] In one or more embodiments, the set of parameters includes a noise variance parameter,
and further includes a precision vector associated with a random variable τ such that
a conditional probability of the support vector in a current iterative update, given
τ, is a joint Gaussian distribution, and a conditional probability of τ itself is
a Gamma distribution with multiple parameters chosen to promote sparse outcomes for
the iteratively-refined estimate.
[0029] In one or more embodiments, the iterative updating of the set of parameters is carried
out over an increasing iteration count which stops as a function of the multiple parameters.
[0030] The above discussion/summary is not intended to describe each embodiment or every
implementation of the present disclosure. The figures and detailed description that
follow also exemplify various embodiments.
BRIEF DESCRIPTION OF FIGURES
[0031] Various example embodiments may be more completely understood in consideration of
the following detailed description in connection with the accompanying drawings, in
which:
FIG. 1A is a system-level diagram of a radar-based object detection circuit, in accordance
with the present disclosure;
FIG. 1B is another system-level diagram of a more specific radar-based object detection
circuit, in accordance with the present disclosure;
FIG. 2 is a signal-flow diagram illustrating an exemplary set of activities for a
system of the type implemented in a manner consistent with FIGs. 1 and 2, in accordance
with the present disclosure;
FIGs. 3A and 3B illustrate, respectively, a set of plots showing effective antenna
spacings and a graph of normalized spatial frequency which may be associated with
a system of the type implemented in a manner consistent with FIGs. 1A, 1B and/or 2
for illustrating aspects of the present disclosure in accordance with the present
disclosure;
FIGs. 4A and 4B are respectively a different set of plots showing effective antenna
spacings and a related graph of normalized spatial frequency, in accordance with the
present disclosure;
FIGs. 5A and 5B are respectively yet another set of plots showing effective antenna
spacings and a related graph of normalized spatial frequency, in accordance with the
present disclosure;
FIG. 6 is a flow chart showing one example manner in which certain more specific aspects
of the present disclosure may be carried out; and
FIGs. 7A and 7B are respective plots comparing numbers of support vectors in a first
known type of iterative process referred to as Sparse Bayesian Learning and in a second
yet type of iterative process which is consistent with example methodology according
to the present disclosure.
[0032] While various embodiments discussed herein are amenable to modifications and alternative
forms, aspects thereof have been shown by way of example in the drawings and will
be described in detail. It should be understood, however, that the intention is not
to limit the disclosure to the particular embodiments described. On the contrary,
the intention is to cover all modifications, equivalents, and alternatives falling
within the scope of the disclosure including aspects defined in the claims. In addition,
the term "example" as used throughout this application is only by way of illustration,
and not limitation.
DETAILED DESCRIPTION
[0033] Aspects of the present disclosure are believed to be applicable to a variety of different
types of apparatuses, systems and methods involving radar systems and related communications.
In certain implementations, aspects of the present disclosure have been shown to be
beneficial when used in the context of automotive radar in environments susceptible
to the presence of multiple objects within a relatively small region. While not necessarily
so limited, various aspects may be appreciated through the following discussion of
non-limiting examples which use exemplary contexts.
[0034] Accordingly, in the following description various specific details are set forth
to describe specific examples presented herein. It should be apparent to one skilled
in the art, however, that one or more other examples and/or variations of these examples
may be practiced without all the specific details given below. In other instances,
well known features have not been described in detail so as not to obscure the description
of the examples herein. For ease of illustration, the same reference numerals may
be used in different diagrams to refer to the same elements or additional instances
of the same element. Also, although aspects and features may in some cases be described
in individual figures, it will be appreciated that features from one figure or embodiment
can be combined with features of another figure or embodiment even though the combination
is not explicitly shown or explicitly described as a combination.
[0035] In a particular embodiment, a radar-based system or radar-detection circuit may include
a radar circuit front-end with signal transmission circuitry to transmit radar signals
and with signal reception circuitry to receive, in response, reflection signals as
reflections from objects which may be targeted by the radar-detection circuit or system.
In processing of data corresponding to the reflection signals, logic or computer-processing
circuitry solves for a sparse array AoA (angle of arrival) estimation problem in which
ambiguities may be recognized and overcome for an accurate AoA estimation. For a more
accurate estimation, the circuitry should also account for measurement errors and
noise, while also respecting data-processing throughput and computation-resource goals
associated with practicable designs.
[0036] In a more specific example, aspects of the present disclosure are directed to overcoming
the estimation problem by carrying out a set of steps which help to account for such
measurement errors and noise by iteratively updating measurement-error and noise parameters,
and by using a matrix-based model in which each of the possible spectrum support vectors
is drawn from a distinct distribution, for example, as may be used in known Sparse
Bayesian models in automatic relevance determination methodologies.
[0037] In a particular embodiment, a radar-based system or radar-detection circuit may include
a multi-input multi-output (MIMO) array, embedded with one or multiple uniform sparse
linear arrays, to process the reflection-related signals. From the MIMO array, output
data is presented as measurement vectors, indicative of signal magnitudes associated
with the reflection signals, to another module for discerning angle-of-arrival (AoA)
information.
[0038] The logic or computer processing circuitry associated with this AoA module determines
or estimates the AoA information by correlating the output data with at least one
spatial frequency support vector indicative of a correlation peak for the output data.
For example, in one specific method, this determination or estimation is realized
by iteratively updating of a set of parameters associated with previous values of
the support vector including a covariance estimate, and a statistical expectation
among a plurality of support vectors (e.g., an average or a median vector or another
middle-ground selection taken from within a limited range such as the mean or median
plus and/or minus seven percent); and pruning, for each iterative update, certain
of the plurality of support vectors having amplitudes which are insignificant relative
to the statistical expectation of the support vector of in a preceding iteration.
[0039] Certain more particular aspects of the present disclosure are directed to such use
and/or design of the AoA module in response to such output data from a multi-input
multi-output (MIMO) array which, as will become apparent, may be implemented in any
of a variety of different manners, depending on the design goals and applications.
Accordingly given that the data flow and related processing operations in such devices
and systems is perceived as being performed in connection with the MIMO array first,
in the following discussion certain optional designs of the MIMO array are first addressed
and then the discussion herein shifts to such particular aspects involving use and/or
design of the AoA module.
[0040] Among various exemplary designs consistent with the present disclosure, one specific
design for the MIMO array has it arranged to include a plurality of embedded sparse
linear arrays, with each such array being associated with a unique antenna-element
spacing from among a set of unique co-prime antenna-element spacings. As will become
apparent, such co-prime spacings refer to numeric value assignments of spacings between
antenna elements, wherein two such values are coprime (or co-prime) if the only positive
integer (factor) that divides both of them is 1; therefore, the values are coprime
if any prime number that divides one does not divide the other. As a method in use,
such a radar-based circuit or system transmits radar signals and, in response, receives
reflection signals as reflections from targeted objects which may be in a particular
field of view. The MIMO virtual array provides processing of data corresponding to
the reflections by using at least two MIMO-embedded sparse linear arrays, each being
associated with one such unique antenna-element spacing. In other designs for the
MIMO array, there are either embedded uniform sparse linear array and/or multiple,
each being associated with a unique antenna-element spacing which may or may not be
necessarily selected from among set of unique co-prime antenna-element spacings.
[0041] These unique co-prime antenna-element spacings may be selected to cause respective
unique grating lobe centers along a spatially discrete sampling spectrum, so as to
facilitate differentiating lobe centers from side lobes, as shown in experiments relating
to the present disclosure. In this context, each sparse linear arrays may have a different
detectable amplitude due to associated grating lobe centers not coinciding and mitigating
ambiguity among side lobes adjacent to the grating lobe centers. In certain more specific
examples also consistent with such examples of the present disclosure, the grating
lobe center of one such sparse linear array is coincident with a null of the grating
lobe center of another of the sparse linear arrays, thereby helping to distinguish
the grating lobe center and mitigate against ambiguous measurements and analyses.
[0042] In various more specific examples, the MIMO virtual array may include various numbers
of such sparse linear arrays (e.g., two, three, several or more such sparse linear
arrays). In each such example, there is a respective spacing value associated with
each of the sparse linear arrays and collectively, these respective spacing values
form a co-prime relationship. For example, in an example wherein the MIMO virtual
array includes two sparse linear arrays, there are two corresponding spacing values
that form a co-prime relationship which is a co-prime pair where there are only two
sparse linear arrays.
[0043] In other specific examples, the present disclosure is directed to radar communication
circuitry that operates with first and second (and, in some instances, more) uniform
MIMO antenna arrays that are used together in a non-uniform arrangement, and with
each such array being associated with a unique antenna-element spacing from among
a set of unique co-prime antenna-element spacings that form a co-prime relationship
(as in the case of a co-prime pair). The first uniform MIMO antenna array has transmitting
antennas and receiving antennas in a first sparse arrangement, and the second uniform
MIMO antenna array has transmitting antennas and receiving antennas in a different
sparse arrangement. The radar communication circuitry operates with the first and
second MIMO antenna arrays to transmit radar signals utilizing the transmitting antennas
in the first and second MIMO arrays, and to receive reflections of the transmitted
radar signals from an object utilizing the receiving antennas in the first and second
MIMO arrays. Directional characteristics of the object relative to the antennas are
determined by comparing the reflections received by the first MIMO array with the
reflections received by the second MIMO array during a common time period. Such a
time period may correspond to a particular instance in time (e.g., voltages concurrently
measured at feed points of the receiving antennas), or a time period corresponding
to multiple waveforms. The MIMO antennas may be spaced apart from one another within
a vehicle with the radar communication circuitry being configured to ascertain the
directional characteristics relative to the vehicle and the object as the vehicle
is moving through a dynamic environment. An estimate of the DOA may be obtained and
combined to determine an accurate DOA for multiple objects.
[0044] The reflections may be compared in a variety of manners. In some implementations,
a reflection detected by the first MIMO array that overlaps with a reflection detected
by the second MIMO array is identified and used for determining DOA. Correspondingly,
reflections detected by the first MIMO array that are offset in angle relative to
reflections detected by the second MIMO array. The reflections may also be compared
during respective instances in time; and used together to ascertain the directional
characteristics of the object. Further, time and/or space averaging may be utilized
to provide an averaged comparison over time and/or space (e.g., after covariance matrix
spatial smoothing).
[0045] In accordance with the present disclosure, FIGs. 1A and 1B are block diagrams to
illustrate examples of how such above-described aspects and circuity may be implemented.
Bearing in mind that aspects of the present disclosure are applicable to a variety
of radar applications which use MIMO-based technology and different modulation schemes
and waveforms, FIG. 1A may be viewed as a generalized functional diagram of a Linear
Frequency Modulation (LFM) automotive MIMO radar involving a radar-based detection
transceiver having a radar circuit and a MIMO virtual array such as described in one
of the examples above.
[0046] More specifically, in the example depicted in FIG. 1A, the radar circuit includes
a front end 120 with signal transmission circuitry 122 to transmit radar signals and
with signal reception circuitry 124 to receive, in response, reflection signals as
reflections from objects (not shown). Antenna elements, as in the examples above,
are depicted in block 126 via dotted lines as part of the front end 120 or as a separate
portion of the radar device. Logic circuitry 130 may include CPU and/or control circuitry
132 for coordinating the signals to and from the front end circuitries 122 and 124,
and may include a MIMO virtual array as part of module 134. In many examples, the
MIMO virtual array provides an output that is used to estimate AoA information and,
therefore, in this example, module 134 is depicted as having a MIMO virtual array
and a detection/measurement aspect.
[0047] After processing via the MIMO virtual array via its sparse linear arrays (each with
unique co-prime antenna-element spacing values), the module 134 may provide an output
to circuitry/interface 140 for further processing. As an example, the circuitry/interface
140 may be configured with circuitry to provide data useful for generating high-resolution
radar images as used by drive-scene perception processors for various purposes; these
may include one or more of target detection, classification, tracking, fusion, semantic
segmentation, path prediction and planning, and/or actuation control processes which
are part of an advanced driver assistance system (ADAS), vehicle control, and autonomous
driving (AD) system onboard a vehicle. In certain specific examples, the drive scene
perception processors may be internal or external (as indicated with the dotted lines
at 140) to the integrated radar system or circuit.
[0048] The example depicted in FIG. 1B shows a more specific type of implementation which
is consistent with the example of FIG. 1A. Accordingly in FIG. 1B, the radar circuit
includes a front end 150 with transmit and receive paths as with the example of FIG.
1A. The transmit path is depicted, as in the upper portion of FIG. 1B, with including
a bus for carrying signals used to configure/program, to provide control information
such as for triggering sending and sampling of send and receive signals and a reference
clock signal which may be used to time-align (or synchronize) such activities between
the transmit and receive paths of the front end 150. These signals are used to transmit
radar signals, via a chirp generation circuit and RF (radio or radar frequency) conditioning-amplification
circuits as are known in many radar communications systems. In the example of FIG.
1B, multiple conditioning-amplification circuits are shown driving respectively arranged
transmit antenna elements within an antenna array block 156. In certain contexts,
the antenna array block 156 may be considered part of or separate from the front end
150.
[0049] The antenna array block 156 also has respectively arranged receive antenna elements
for receiving reflections and presenting corresponding signals to respective amplifiers
which provide outputs for subsequent front-end processing. As is conventional, this
front-end processing may include mixing (summing or multiplying) with the respective
outputs of the conditioning-amplification circuits, high-pass filtering, further amplification
following by low-pass filtering and finally analog-to-digital conversion for presenting
corresponding digital versions (e.g., samples) of the front end's processed analog
signals to logic circuitry 160.
[0050] The logic circuitry 160 in this example is shown to include a radar controller for
providing the above-discussed control/signal bus, and a receive-signal processing
CPU or module including three to five functional submodules. In this particular example,
the first three of these functional submodules as well as the last such submodule
(which is an AoA estimation module as discussed with FIG. 1A) are may be conventional
or implemented with other advancements. These first three submodules are: a fast-time
FFT (fast-Fourier transform) block for generating object-range estimations and providing
such estimations to a range-chirp antenna cube; a slow-time FFT block for Doppler
estimations as stored in range-Doppler antenna cube; and a detection block which uses
the previous block to generate data associated with objects detected as being in (range-Doppler)
cells.
[0051] The fourth submodule in this example is a MIMO co-prime array module which, as discussed
above, may be implemented using at least two MIMO-embedded sparse linear arrays, each
being associated with one such unique antenna-element spacing, such as with values
that manifest a co-prime relationship.
[0052] Consistent with the logic circuitry 160, FIG. 2 is a block diagram showing data flow
for a LFM MIMO automotive radar receiver and specifically for the processing chain
for data from the ADC data signal such as in FIG. 1B. Upon receiving the ADC sample
stream from the radar transceiver, the chirp data is first processed for range spectrum
using FFT accelerators, and the accumulated range-chirp map then processed over the
chirp dimension with another FFT to produce Doppler spectrum and produces the produce
Range Doppler map for each channel. Detection may use any of various implementations
such as via a CFAR (adaptive constant false alarm rate) algorithm to detect the presence
of targets in certain cells. For each detected range-Doppler cell, the MIMO virtual
array may be constructed according to specific MIMO waveform processing requirements
and may be used to produce an array measurement vector that is ready for AoA estimation
processing. Such an AoA Estimator may then process the array measurement vector and
produce target position information for use by subsequent circuits or systems (e.g.,
for data logging, display, and downstream perception, fusion, tracking, drive control
processing).
[0053] In such examples using such a memory array (e.g., MIMO) for a co-prime array, as
in the module of the logic circuitry 160, an advantageous aspect of concerns the suppression
of spurious sidelobes as perceived in the spatial resolution spectrum in which the
amplitudes of main lobes or "grating lobes" are sought to be distinguished and detected.
Spurious sidelobes are suppressed by designing the MIMO co-prime array module as a
composite array including at least two uniform linear arrays (ULA) with co-prime spacings.
By using co-prime spacing, ambiguities caused by the sidelobes are naturally suppressed.
The suppression grows stronger when the composite ULA is extended to larger sizes
by adding additional MIMO-based transmitters via each additional ULA, as the suppression
of spurious sidelobes may be limited by the size of the two composite ULAs. In the
cases where higher suppression is desirable to achieve better target dynamic range,
further processing may be implemented.
[0054] In experimentation/simulation efforts leading to aspect of the present disclosure,
comparisons of a 46-element uniform linear array (ULA) and a 16-element sparse array
(SPA) of 46-element aperture has shown that the SPA and ULA have similar aperture
parameters but the spatial under sampling of the SPA results in many ambiguous spurious
sidelobes, and that further reducing the amplitudes of the spurious sidelobes results
in a significant reduction of targets (or object) being falsely identified and/or
located. In such a spatial resolution spectrum, the amplitude peaks in the spectrum
corresponds to detected targets.
[0055] A more specific example of the present disclosure is directed to further mitigating
the spurious sidelobe issues by setting up the issues using probability theories having
related probability solutions. Using the sparsity constraint imposed upon the angular
spectrum, such issues are known as L-1 Norm minimization problems. Well-known techniques
such as Orthogonal Matching Pursuit (OMP) may be used for resolving the sparse angular
spectrum; however, the performance is impacted by the sensitivity to array geometry
and support selection, sensitivity to angle quantitation, and/or the growing burden
of least-squares (LS) computation as more targets are found. Alternatively and as
a further aspect of the present disclosure, such performance may be improved by mitigating
the angle quantization problem to a large degree by carrying out a set of steps which,
as noted above, help to account for measurement errors and noise by iteratively updating
measurement-error and noise parameters. These steps may use a matrix-based model in
which each of the possible spectrum support vectors is drawn from a distinct distribution,
for example, as may be used in known Sparse Bayesian Models in automatic relevance
determination methodologies.
[0056] Before further discussing these steps, the discussion first explains how such a MIMO
array may be used, according to various optional aspects of the present disclosure,
to develop and generated the output data used by the AoA estimation module (e.g.,
134 of FIG. 1A or as within block 160 of FIG. 1B). One such aspect concerns the extendibility
of such a MIMO co-prime sparse array. For MIMO radars, AoA estimation is based on
the reconstructed MIMO virtual array's outputs. In a MIMO radar system, the equivalent
position of a virtual antenna element can be obtained by summing the position vectors
of the transmitting antenna and receiving antenna. As the result, the virtual array
consists of repeating antenna position patterns of the Rx antenna array centered at
the Tx antenna positions (or vice versa). Because of the array geometry repeating
nature, for MIMO radar system, it is not possible to construct arbitrary sparse array
pattern. With this limitation of reduced degrees of freedom, the sidelobe suppression
becomes more difficult.
[0057] Optionally, the above-described MIMO array may be constructed to result in sidelobe
suppression being repeatable (i.e., extendable via MIMO Tx) antenna geometry. The
constructed MIMO virtual array consists of 2 embedded ULAs each with a unique element
spacing. First, the two element spacing values are selected such that they are coprime
numbers (that is, their greatest common factor (GCF) is 1 and their lowest common
multiple (LCM) is their product). Secondly, the co-prime pair is selected such that
the two composite ULA's results in an array of a (sparse) aperture of the size equal
to the LCM and of antenna elements equal to the number of physical Rx antenna elements
plus 1. If such array is found, the composite-ULA array can then be repeated at every
LCM elements by placing the MIMO TX's LCM elements apart.
[0058] For example, for a system of 8 physical Rx antennas and 2 Tx MIMO antennas, a co-prime
pair {4, 5} is selected to form the composite-ULA sparse array based on the following
arrangement. This is shown in the table below:
Element position: |
0 4 5 8 10 12 15 16 20 |
4-element spacing ULA: |
x _ _ _ x _ _ _ x _ _ _ x _ _ _ x _ _ _ x |
5-element spacing ULA: |
x _ _ _ _ x _ _ _ _ x _ _ _ _ x _ _ _ _ x |
{4,5} Composite-ULA SPA: |
∘ _ _ _ ∘ ∘ _ _ ∘ _ ∘ _ ∘ _ _ ∘ ∘ _ _ _ ∘ |
Rx Element Index: |
1 2 3 4 5 6 7 8 9 |
[0059] The LCM of {4, 5} co-prime numbers is 20, so, by placing MIMO Tx (transmit, as opposed
to Rx for receive) antennas at {0, 20, 40,...} element positions (i.e. integer multiples
of LCM), the two ULAs can be naturally extended to form a larger composite-ULA sparse
array. This requires careful selection of the co-prime pair. The case of 2 Tx {4,
5} co-prime sparse array can be constructed based on the following arrangement, where
the locations of the Tx antennas is marked with 'T' and the locations of the Rx antennas
are marked with 'R'. The constructed MIMO virtual antennas' locations are marked with
'V'. The virtual array may consist of 2 embedded ULAs of 4 and 5 element spacings,
both with the same (sparse array) aperture size of 36 elements, as below.
Position: |
0 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 16 _ _ _ 20 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ |
36 |
|
Tx: |
T _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ T |
Rx: |
R _ _ _ R R _ _ R _ R _ R _ _ R R _ _ _ _ |
Virtual: |
V _ _ _ V V _ _ V _ V _ V _ _ V V _ _ _ V _ _ _ V V _ _ V _ V _ V _ _ V |
V |
|
[0060] Assuming half-wavelength element spacing, for a filled ULA the grating lobe occurs
in the angle spectrum outside the +/- 90° Field of view (FOV) so no ambiguity occurs.
On the other hand, for the 4-element spacing ULA and the 5-element spacing ULA, grating
lobe occurs within the +/- 90° FOV causing ambiguous sidelobes. The use of coprime
element spacings, however, effectively reduces the amplitude level of the ambiguous
sidelobes because the centers of the grating lobes of the two co-prime ULAs do not
coincide until many repeats of the spatially discretely sampled spectrums. Because
the centers of the grating lobes from the two ULAs do not overlap, the composite grating
lobes have a lowered amplitude level due to the limited lobe width. Further, not only
the centers of the grating lobes do not overlap, the center of the grating lobe of
the first ULA coincide with a null of the second ULA such that it is guaranteed that
the power from the two ULAs do not coherently add up in the composite array. This
directly results in the suppression of the grating lobes in the composite array. As
more MIMO Tx's are employed to extend the ULAs, the lobe width is further reduced
such that the composite grating lobe levels are further reduced. Thus, aspects of
the present disclosure teach use of a sparse MIMO array construction method that is
sure to reduce the ambiguous sidelobes (or composite grating lobes of the co-prime
ULAs) and the sidelobe suppression performance scales with the number of MIMO Tx's
employed. Note that when more MIMO Tx's are employed, the overlap of the grating lobes
further decreases. The co-prime pair guarantees a suppression level of roughly 50%.
Additional suppression can be achieved by further incorporating additional co-prime
ULA(s). For example, {3, 4, 5} are co-prime triplets which suppresses grating lobes
to roughly 30% of its original level. {3, 4, 5, 7} are co-prime quadruplets which
suppresses grating lobes to roughly 25% of its original level, etc. The percentage
of suppression corresponds to the ratio of the number of elements of a co-prime ULA
and the total number of elements in the composite array.
[0061] Further understanding of such aspects of the present disclosure may be understood
by way of further specific (non-limiting) examples through which reference is again
made to the spatial resolution spectrum but in these examples, with spatial frequency
plots being normalized. These specific examples are shown in three pairs of figures
identified as: FIGs. 3A and 3B; FIGs. 4A and 4B; and FIGs. 5A and 5B. For each pair
of figures, the upper figure of the pair first shows the composite SPA with an effective
random spacing as implemented by the following two or more ULA's for which the spacing
values are based on the co-prime pairing or co-prime relationship as discussed above.
The lower figure of the pair shows a plot of the relative measurements of the lobes
positioned over a horizontal axis representing the normalized spatial frequency plots
respectively corresponding to the composite SPA and its related ULA's with the noted
spacings.
[0062] In FIGs. 3A and 3B, a {4, 5} co-prime sparse array of 8 elements is depicted. The
composite SPA corresponds to spacing 310 and plot 340, and the two ULAs for which
the antenna element spacing values are 4 (312) and 5 (314) are depicted as corresponding
to plots 342 and 344. The co-prime ULA angle spectrums are illustrated in which the
noncoincident grating lobes can be seen with partial overlap at 350 and 352 of FIG.
3B. It can also be observed that the grating lobes of one ULA coincides with nulls
of the other ULA's (at 356 and 358 of FIG. 3B) showing significance of the sidelobe
suppression effect. The resulting grating lobe in the composite array is about half
of the origin amplitude.
[0063] FIGs. 4A and 4B illustrate a 2-Tx MIMO extended {4,5} co-prime sparse array which
is used to produce a 16-element co-prime array. The 16-element co-prime array is realized
using an extension of the co-prime ULAs by way of an additional MIMO (transmit array)
as seen at the top of FIG. 4A. The composite SPA, having the additional MIMO, corresponds
to spacing 410 and plot 440, and the two ULAs for which the antenna element spacing
values are 4 (412) and 5 (414) are depicted as corresponding to plots 342 and 344.
It can be seen that the grating lobe's beam width is halved (at 450 and 452) such
that the amount of overlap is reduced. The resulting composite array angle spectrum
not only has further suppressed grating lobes, but they are also more distinctly identifiable
for resolving/mitigating false detections in connection with later sparse array processing
steps.
[0064] In FIGs. 5A and 5B, a {3, 4, 5} co-prime sparse array is illustrated which produces
a 11-element co-prime array. It can be seen that the grating lobe's level is suppressed
further (at 550 and 552) with this extension of a third sparse array. The composite
SPA corresponds to spacing 510 and plot 540, and the three ULAs for which the antenna
element spacing values are 3 (512), 4 (514) and 5 (516) are depicted as corresponding
to plots 542, 544 and 546. The number of embedded sparse ULAs may include, for example,
between three and six (or more) embedded sparse linear arrays
[0065] In other examples, relative to the example of FIG. 3A and 3B, the number of ULA'
may be increased (as in FIGs. 5A and 5B) and the number of extension(s) may be increased
(as in FIGs. 4A and 4B)
[0066] One may also compute individual co-prime ULA angle spectrums and detect angle-domain
targets separately for each spectrum. In such an approach, only targets detected consistently
in all co-prime ULA spectrums may be declared as being a valid target detection. In
such an embodiment which is consistent with the present disclosure, the individual
co-prime ULA's AoA spectrum are first produced and targets are identified as peaks
above a predetermined threshold. Next, detected targets are check if they are present
in the same angle bin in all co-prime ULAs' spectrums. If it is consistently detected
in the same angle bin of all spectrums, a target is declared. Otherwise it is considered
as a false detection and discarded.
[0067] In general, conventional processing for AoA estimation effectively corresponds to
random spatial sampling and this leads to a sparse array design. It can be proven
that the maximum spurious sidelobe level is proportional to the coherence so it follows
that by designing a matrix A that has low coherence, this leads to low spurious sidelobes
and vice versa. This demonstrates that by employing the extendable MIMO co-prime array
approach of the present disclosure, reduced coherence can be achieved, and sparse
recovery of targets can be obtained using greedy algorithms. In this context, such
above-described MIMO array aspects are complemented by addressing the sparse spectral
signal linear regression problem.
[0068] More specifically, to process the output of a sparse array, standard beamforming
or Fourier spectral analysis based processing suffers due to the non-uniform spatial
sampling which violates the Nyquist sampling rules. As a result, high spurious angle
sidelobes will be present alone with the true target beams. To mitigate the spurious
sidelobes, one may impose sparsity constraints on the angle spectrum outputs and solve
the problem accordingly. One class of algorithms, based on so called greedy algorithms,
originally developed for solving underdetermined linear problems, can be used for
estimating the sparse spectrum output.
[0069] As is known the greedy algorithm starts by modelling the angle estimation problem
as a linear regression problem, that is, by modelling the array output measurement
vector
x as a product of an array steering matrix
A and a spatial frequency support amplitude vector
c plus noise
e, where each column of
A is a steering vector of the array steered to a support spatial frequency (
f1,
f1,...
fM) in normalized unit (between 0 and 1) upon which one desires to evaluate the amplitude
of a target and the spatial sampling positions (
t1,
t1,...
tN) in normalized integer units. To achieve high angular resolution, a large number
of supports can be established, thereby dividing up the 0∼2π radian frequency spectrum
resulting in a fine grid and a "wide"
A matrix (that is, number of columns, which corresponds to the number of supports,
is much greater than the number of rows, which corresponds to the number of array
outputs or measurements). Since
A is a wide matrix, this implies that the number of unknowns (vector
c) is greater than the number of knowns (vector x) and the solving of equation
x = Ac + e is an under-determined linear regression problem, where
x and
e are N×1 vectors,
A is a NxM matrix, and
c is a M×1 vector . This is seen below as:

[0070] Next, the greedy algorithm identifies one or more most probable supports and assuming
one such most probable support, measures this support's most probable amplitude, and
this is followed by cancellation of its contribution to the array output measurement
vector to obtain a residual array measurement vector
r. Based on the residual measurement vector, the process repeats until all supports
are found or a stop criteria is met.
[0071] The identification of the most probably support (without loss of generality, assume
one support is to be selected at a time) is by correlating the columns of
A with measurement vector and support frequency that leads to the highest correlation
is selected. The correlation vector,
y, can be directly computed by
y = AHx for the first iteration where
AH denotes the transpose-conjugate (i.e. Hermitian transpose) of
A. In general, for the k-th iteration, the correlation output is computed as
y = AHrk where
rk is the residual measurement vector computed in the k-1-th iteration and
r1 =
x. The found support of the k-th iteration is then added to a solution support set
s ∈ {
i1,
i2, ...
ik}.
[0072] The amplitude of the found support and the residual measurement vector can be obtained
in any of various versatile ways. One known method, known as Matching Pursuit or MP,
involves an iterative search through which the correlator peak's amplitude is found,
and the amplitude is simply selected as the correlator peak's amplitude. Another known
method, known as Orthogonal Matching Pursuit or OMP, in which a least-squares (LS)
fitted solution is selected as the amplitude. The LS-fit is based on solving a new
equation
x = Ascs in LS sense, where
As consists of columns of A of selected support set and elements of
cs is a subset of elements of c of the selected supports. Once the amplitudes are found,
the residual measurement vector is updated by
rk+1 = x - Asĉs where
ĉs is the LS solution of
cs. One solution to the LS problem is simply the pseudo inverse from which
ĉs is solved by

(for square or narrow matrix
As) or

(for wide matrix A
s).
[0073] The MP and OMP method can be used to reconstruct the sparse spectrum
c if a certain property of
A is met. One of such widely used property is Coherence,
µ(
A), defined by the equation

, where
Ai and
Aj are the i-th and the j-th column of
A, respectively and in theory,

. According to the known theory, unique sparse reconstruction is guaranteed if

where K denotes the number detectable targets (i.e. number of supports with amplitude
above noise level). So, the lower the Coherence, the large value of
K is possible. Note that unique reconstruction is possible if such condition is not
met, only that it cannot be guaranteed based on the known theory.
[0074] In order to achieve high angular resolution, many supports much more than the number
of measurements (i.e. N<<M) is modelled and estimated. This naturally leads to very
high Coherence which in turn results in small K or recoverable target amplitudes.
One way to reduce the Coherence is by randomizing the spatial sampling of the steering
vectors. For example, one may create a N'×1 steering vector where N' > N, and randomly
(following any sub-Gaussian or Gaussian probability distribution) deleting the samples
to obtain a N×1 vector. The resulting matrix is called Random Fourier matrix. In the
following equation, the matrix
A represents such a Random Fourier matrix where {
t1,
t2, ...,
tN} are
N integers randomly selected from {0,1, ...,
N'}.

[0075] In general, the random spatial sampling requirement leads the sparse array design
and it can be proven that the maximum spurious sidelobe level is proportional to the
Coherence so by designing a matrix
A that has low Coherence leads to low spurious sidelobes and vice versa. This demonstrates
that by employing the extendable MIMO coprime array approach of the present disclosure
previously introduced, reduced Coherence can be achieved, and sparse recovery of targets
can be obtained using greedy algorithms.
[0076] One problem with a greedy algorithm arises from the quantized supports on which target
amplitudes are evaluated. Given finite quantization, which is necessary to keep coherence
low, it is not possible to always have signals coincide exactly with the spatial frequency
of the supports. When the actual spatial frequency misaligns with any of the supports,
it may not be possible to cancel the target signal in its entirety in the residual
measurement vector and as a result, neighboring supports are to be selected in order
to cancel the signal in the later iteration(s). The resulting solution becomes non-sparse
and the sparse recovery performance; thus, the resolution performance, is degraded.
[0077] Returning now to the AoA estimation determination and use of the iterativelyexecuted
steps or actions to account for measurement error and noise, another aspect of the
present disclosure involves an initialized array steering matrix used to model the
angle estimation problem, and for which a solution may be provided through a sparse
learning method which has a pruning action carried out in connection with each iteration
to rule out supports that are of insignificant amplitude based on previous estimation
of the spectrum amplitudes (e.g., as estimated in one or more of the immediately preceding
iterations). According to examples of the present disclosure, aspects of the sparse
learning methodology is best understood using certain probability theories which are
common to Bayesian Linear Regression (BLR) approaches as discussed below.
[0078] In BLR, the problem of finding sparse
c is modeled as the problem of finding the most probable values of
c given the measurement
x, corrupted by random noise
ε. In other words,
c is estimated by finding the values of
c that maximize the posterior probability
p(
c|x), which can be casted into a simpler problem based on Bayesian theorem, following the
max a posteriori (MAP) estimator approach shown as follows:
ĉ = arg
maxc p(
c|
x) =

.
[0079] In order to find solution of above problem, one may establish some prior knowledge
on the probability distribution p(
c) and
p(
x|
c). For AoA estimation problems of radar systems, the conditional probability of
p(
x|
c) carries the physical meaning of array measurement noise, which can be modeled as
a joint distribution of i.i.d zero-mean Gaussian random variables. As to the selection
of the distribution of p(
c), there are a variety of a versatile of ways to model it such that the resulting
estimate on
c is sparse, and Sparse Bayesian Learning (SBL) is an example.
[0080] SBL models p(c) by introducing a latent random variable τ such that the conditional
probability
p(c|τ) is a joint Gaussian distribution and further assuming that
p(τ) itself is a Gamma distribution with parameters {
α,
β} whose value is chosen by the model designer. In the context of SBL, it is favorable
to set {
α,
β} →- {0,0} such that the resulting p(c) has a long-tail distribution having a general
form of

which is robust to outliers thus it promotes sparse solutions (i.e. zero, i.e. noise,
is the most probably value with or without the presence of outliers, i.e. target signals).
The exact model of the SBL is provided below, with the measurement error being modeled
as Gaussian:

[0081] The a priori distribution is modeled as a marginal distribution with the following
form:

where

such that elements of c follows the Student's t distribution,

which tends to the form

when
α →- 0,
β →- 0.
[0082] With reference to the above relationships, ĉ = arg
maxc In
p(x|c) + In p(c) may be solved using above definitions. One may compute the derivative
of ln
p(y|c) + In p(c) w.r.t c and set it to zero such that
c can be found, along with distribution parameters

and τ also found through maximizing

.
[0083] In certain more specific examples and while detailed derivations may be known, c
may be iteratively found by sequentially updating equations as below with initial
values of
ĉ set according to an FFT beamforming result,

set to a value close to noise variance and wherein
τ̂i is set to suitable identical values such that it cannot be neglected in
Ω nor does it dominates
Ω.
Update covariance of c given y: |

|
Update mean of c given y (output spectrum): |

|
Update noise variance: |

|
Update precision vector: |

|
[0084] Disadvantages in using SBL are well known and they include its performance. As an
example, SBL requires an inversion step in the
Ω update and this inversion often leads to numerical problems when

tends towards small values. When this occurs, the low rank
AHA term dominates the expression which results in a rank deficiency problem for the
matrix inverse. Secondly, the MxM matrix to be inverted can be very large and this
results in computation efficiency being correspondingly low.
[0085] Certain aspects of the present disclosure may be used to mitigate such disadvantages
of SBL, and one, as mentioned above, is the pruning action carried out in connection
with each iteration to rule out supports that are of insignificant amplitude. This
may be based on one or more previous estimations of the spectrum amplitudes. The effect
is a result which decreases the size of the problem monotonically with each new iteration.
In turn, this reduces the computation burden and also well reduces the sensitivity
to the rank deficiency problem.
[0086] Further, in a typical implementation according to the present disclosure, there is
no matrix inversion step as such. Rather, instead of a matrix inversion step as above,
Cholesky decomposition is used to take advantage of the structure of the underlying
matrix to be inverted such that the speed increases and the computation is more robust
against numerical issues. The enhanced solution is described in the below equations
where
ĉp is the amplitude after the pruning and
Ap is the corresponding steering vector matrix of the pruned support. Matrix
U is the upper triangular matrix based on the Cholesky decomposition.
Cholesky decompose objective matrix: |

|
Update covariance of c given y: |

|
Update mean of c given y (output spectrum): |

|
Update noise variance: |

|
Update precision vector: |

|
[0087] As an illustration in accordance with yet a specific example, the present disclosure
includes FIG. 6 as a flow chart showing one example manner for implementing such methodology.
Again, these operations may be implemented by logic circuitry such as in the AoA-related
module shown at the lower right of FIG. 1A and/or FIG. 1B, assuming the circuits being
used align these illustrated examples. In other examples according to the present
disclosure, such aspects may be implemented in different manners such as in circuits
external to the radar front end circuitry and/or in a manner integrated with such
above-described and other aspects and actions.
[0088] For purposes of understanding some of the terminology, this flow in FIG. 6 pertains
to the above type of steering vector matrix
Ap of full supports. In practice, the entire matrix need not to be precomputed and stored
and can be generated on the fly and/or on demand. This specific example process may
be carried out as follows.
[0089] At the top of FIG. 6, flow begins at block 610 with initialization of a count variable
p which may be used to track the iterations or times through the flow of FIG. 6 and
which may be reset to 0, and an initialization of certain vector-related parameters
to be updated which, in this example, are: the noise variance parameter, the precision
vector, and the output support amplitude vector
ĉp (to be the amplitude after the pruning) which is initialized to

. As should be apparent, these vector-related parameters to be updated refer to the
variables, terms and mathematical relationships as discussed above in connection with
the related aspects of the present disclosure.
[0090] The next several blocks of FIG. 6 are performed, in this example, before the flow
would generate an output or report of a determination of the AoA. Accordingly, from
block 610, flow proceeds to block 620 where vector supports are pruned as indicated
above and in the illustrated block 620. From block 620, flow proceeds to block 625
where the objective matrix is simplified via a Cholesky decomposition, as above and
illustrated. From block 625, flow proceeds to block 630 where the logic circuitry
updates the covariance of the output support amplitude vector as indicated and illustrated.
From block 630, flow proceeds to block 640 where the logic circuitry updates the support
amplitude vector
ĉp as indicated and illustrated. From block 640, flow proceeds to block 650 where the
logic circuit computes the normalized residual r
p based on an absolute value associated with the above updates and processing, and
this is where a residual vector may be stored for a comparison step in connection
with the determination associated with the next block 660. This residual vector may
be used to reflect measurement error taken from a Gaussian distribution.
[0091] In block 660, a decision is made based on whether the residual vector has been reduced
below a minimum residual threshold
rTH or whether a maximum iteration count threshold for the count p is equal to
pmax. This decision is processed to assess whether a stop criteria is realized (in this
example, the thresholds
pmax and
rTH)
. If either of these conditions is met, flow proceeds from block 660 to block 665 where
the logic or computer circuitry effects a report as noted above; otherwise, flow proceeds
from block 660 to block 670 where the noise variance parameter is updated as indicated
and illustrated in block 670.
[0092] From block 670, flow proceeds to block 680 where the precision vector, as yet another
parameter, is updated as indicated and illustrated in block 680. Next, at block 690,
the count p is incremented and flow returns to block 620 supports being pruned for
the next iteration in the flow shown in this example of FIG. 6.
[0093] In example experimental and/or simulation-based implementations, consistent with
the above aspects of the present disclosure, AoA estimation results have been obtained
for two type of virtual (e.g., MIMO) arrays: a 16-element {4,5} co-prime sparse array
and a 16-element uniform linear array (ULA). The results show that the targets may
be resolved using either array configuration. When the sparse array is used, better
resolution performance is shown to be usually achieved. When ULA is used, the performance
loss is observed however it is not lost entirely like greedy algorithm methods. This
demonstrates that such aspects of the present disclosure result in superior sparse
spectral signal reconstruction. From these implementations, such results also show
that the spectral peaks are generally wider than other greedy algorithms and, depending
on the greedy algorithm, this may be due to its probabilistic modelling of the spectrum
amplitudes.
[0094] For a simulated example in which 6 targets are present, FIG. 7A and FIG. 7B illustrate
the number of supports solved in each iteration for a conventional SBL approach (FIG.
7A) and a pruning-type sparse learning (FIG. 7B) as discussed in connection with the
above aspects of the present disclosure. The number of supports are pruned for the
case of pruning-type sparse learning (FIG. 7B) and it is monotonically reduced from
256 to 26 which means that the matrix that may be inverted (for the case of the SBL
approach) or Cholesky decomposed (for the case of pruning-type sparse learning of
FIG. 7B) can differ by as much as 10 times, resulting in difference in computation
as much as 1000 times (based on O{
n3}) in the final iterations. The use of Cholesky decomposition (sometimes QR decomposition)
can be more efficient (depending on the implementation) and it also reduces the sensitivity
to rank deficiency so in general the robustness of the present disclosure is improved.
[0095] Accordingly in accordance with the present disclosure, such a pruning-type sparse
learning method may be applied for processing output data indicative of reflection
signals passed from a sparse array, and such an array may be in any of a variety of
different forms such as those disclosed as above. In each instance, the logic (or
processing) circuitry receives the output data as being indicative of signal magnitude
(e.g., in a spectrum support vector) of the reflection signals via the sparse array,
and then discerns angle-of-arrival information for the output data by performing certain
steps in an iterative manner for implementation of a sparse learning method which
includes pruning, for each iterative update, certain of the plurality of spectrum-related
support vectors having respective amplitudes which are insignificant relative to the
statistical expectation of the support vector in a preceding iteration.
[0096] In certain more-specific examples according to the present disclosure, these steps
include updating of a set of support-vector parameters including a covariance estimate
of the support vector, and a statistical expectation of the support vector over a
plurality of spectrum-related support vectors (e.g., mean). In related more-specific
examples, the above-noted set of parameters to be updated with each iteration (e.g.,
associated with previous values of the support vector) may include a covariance estimate
of the support vector, a statistical expectation of the support vector over a plurality
of spectrum-related support vectors, a noise variance associated with the most recent
refinement of the support vector, and a scaling parameter such as τ as exemplified
above. Further and as applicable to each such example, to reduce further computational
burdens which may be significant for many computer-circuit architectures, the matrix-based
model may also be processed by Cholesky decomposition with each iterative update.
[0097] Terms to exemplify orientation, such as upper/lower, left/right, top/bottom and above/below,
may be used herein to refer to relative positions of elements as shown in the figures.
It should be understood that the terminology is used for notational convenience only
and that in actual use the disclosed structures may be oriented different from the
orientation shown in the figures. Thus, the terms should not be construed in a limiting
manner.
[0098] As examples, the Specification describes and/or illustrates aspects useful for implementing
the claimed disclosure by way of various circuits or circuitry which may be illustrated
as or using terms such as blocks, modules, device, system, unit, controller, etc.
and/or other circuit-type depictions. Such circuits or circuitry are used together
with other elements to exemplify how certain embodiments may be carried out in the
form or structures, steps, functions, operations, activities, etc. As examples, wherein
such circuits or circuitry may correspond to logic circuitry (which may refer to or
include a code-programmed/configured CPU), in one example the logic circuitry may
carry out a process or method (sometimes "algorithm") by performing such activities
and/or steps associated with the above-discussed functionalities. In other examples,
the logic circuitry may carry out a process or method by performing these same activities/operations
and in addition.
[0099] For example, in certain of the above-discussed embodiments, one or more modules are
discrete logic circuits or programmable logic circuits configured and arranged for
implementing these operations/activities, as may be carried out in the approaches
shown in the signal/data flow of FIGs. 1A, 1B and 2. In certain embodiments, such
a programmable circuit is one or more computer circuits, including memory circuitry
for storing and accessing a program to be executed as a set (or sets) of instructions
(and/or to be used as configuration data to define how the programmable circuit is
to perform), and an algorithm or process as described above is used by the programmable
circuit to perform the related steps, functions, operations, activities,
etc. Depending on the application, the instructions (and/or configuration data) can be
configured for implementation in logic circuitry, with the instructions (whether characterized
in the form of object code, firmware or software) stored in and accessible from a
memory (circuit). As another example, where the Specification may make reference to
a "first" type of structure, a "second" type of structure, where the adjectives "first"
and "second" are not used to connote any description of the structure or to provide
any substantive meaning; rather, such adjectives are merely used for English-language
antecedence to differentiate one such similarly-named structure from another similarly-named
structure.
[0100] Based upon the above discussion and illustrations, those skilled in the art will
readily recognize that various modifications and changes may be made to the various
embodiments without strictly following the exemplary embodiments and applications
illustrated and described herein. For example, methods as exemplified in the Figures
may involve steps carried out in various orders, with one or more aspects of the embodiments
herein retained, or may involve fewer or more steps.
1. An apparatus comprising:
a radar circuit to receive reflection signals, in response to transmitted radar signals,
as reflections from objects; and
computer processing circuitry to process data corresponding to the reflection signals
via a memory array and, in response, to generate output data indicative of signal
magnitude associated with the reflection signals, and to discern angle-of-arrival
information for the output data by correlating the output data with an iteratively-refined
estimate of a sparse spatial frequency support vector ("support vector") indicative
of a correlation peak for the output data, the iteratively-refined estimate generated
by:
iteratively updating of a set of parameters associated with previous values of the
support vector including a covariance estimate of the support vector, and a statistical
expectation of the support vector over a plurality of spectrum-related support vectors;
and
pruning, for each iterative update, certain of the plurality of spectrum-related support
vectors having respective amplitudes which are insignificant relative to the statistical
expectation of the support vector derived in a preceding iteration.
2. The apparatus of claim 1, wherein the sparse spatial frequency support vector is processed
as a random variable using a matrix-based model, and wherein the matrix-based model
is processed by Cholesky decomposition with each iterative update.
3. The apparatus of any of the preceding claims, wherein the set of parameters includes
a noise variance parameter, wherein the sparse spatial frequency support vector is
processed as a random variable using a matrix-based model, and wherein the steps are
carried out sequentially, without inversion of a matrix in the matrix-based model,
with the update of the statistical expectation of the support vector following the
update of the covariance estimate of the support vector, and an update of the noise
variance parameter following the update of the statistical expectation of the support
vector.
4. The apparatus of any of the preceding claims, wherein the set of parameters includes
a noise variance parameter and further includes a precision vector associated with
a random variable τ such that a conditional probability of the support vector in a
current iterative update, given τ, is a joint Gaussian distribution, and a conditional
probability of τ itself is a Gamma distribution with multiple parameters chosen to
promote sparse outcomes for the iteratively-refined estimate.
5. The apparatus of claim 4, wherein the iterative updating of the set of parameters
is carried out over an increasing iteration count which stops as a function of the
multiple parameters.
6. The apparatus of any of the preceding claims 1 to 4, wherein the iterative updating
of the set of parameters is carried out over an increasing iteration count which stops
as a function of a measurement error having a Gaussian distribution.
7. The apparatus of claim 6, wherein the measurement error corresponds to a probability
of error given the support vector after its most recent iterative update.
8. The apparatus of any of the preceding claims, wherein the computer processing circuitry
is to iteratively update the set of parameters over an increasing iteration count
which ceases upon reaching or satisfying a threshold criteria and, in response, to
the threshold criteria, generate resultant data corresponding to the discerned angle-of-arrival
information for the output data.
9. The apparatus of any of the preceding claims, wherein the statistical expectation
corresponds to a mean, or average of the plurality of spectrum-related support vectors
associated with a current iteration.
10. The apparatus of any of the preceding claims 1 to 8, wherein the statistical expectation
corresponds to a range corresponding to a subset of the plurality of spectrum-related
support vectors associated with a current iteration, wherein the subset accounts for
or includes a mean.
11. The apparatus of any of the preceding claims, wherein the memory array is or includes
a multi-input multi-output virtual array has at least one embedded uniform sparse
linear arrays being associated with a unique antenna-element spacing.
12. The apparatus of any of the preceding claims 1 to 10, wherein the memory array is
or includes a multi-input multi-output virtual array having at least two embedded
uniform sparse linear arrays, each of which is being associated with a unique antenna-element
spacing from among a set of unique co-prime antenna-element spacings.
13. The apparatus of any of the preceding claims, wherein the radar circuit includes sets
antenna elements spaced for radar signal transmissions and in response, reception
of reflections from the radar signal transmissions.
14. The apparatus of any of the preceding claims 1 to 12, wherein the radar circuit includes
front-end analog circuitry for radar signal transmissions and in response, reception
of reflections from the radar signal transmissions, and further includes analog-to-digital
and/or digital-to-analog conversion circuitry to communicatively couple the front-end
analog circuitry with the computer processing circuitry.
15. A method for use in an apparatus which includes a radar circuit and computer processing
circuitry, the method comprising:
receiving, in response to transmitted radar signals, reflection signals as reflections
from objects; and
in the computer processing circuitry,
processing data corresponding to the reflection signals via a memory array,
generating, in response, output data indicative of signal magnitude associated with
the reflection signals, and
discerning angle-of-arrival information for the output data for the output data by
correlating the output data with an iteratively-refined estimate of a sparse spatial
frequency support vector ("support vector") indicative of a correlation peak for the
output data, the iteratively-refined estimate generated by:
iteratively updating of a set of parameters associated with previous values of the
support vector including a covariance estimate of the support vector, and a statistical
expectation of the support vector over a plurality of spectrum-related support vectors;
and
pruning, for each iterative update, certain of the plurality of spectrum-related support
vectors having respective amplitudes which are insignificant relative to the statistical
expectation of the support vector of in a preceding iteration.